

Here \(p^n\)  is the body's position in the navigation frame, \(v^n\)  is
the velocity, \(g^n\)  is the
local gravityThe centrifugal acceleration due to the earth's
rotation is assumed to be included in the local gravity
vector [1]}., \(\omega ^b\)  is the angular velocity between the navigation
frame and the body frame, and \(s^b\)  is the
specific force at the origin of the body
frame. The superscripts \(n\)  and \(b\)  denote the navigation and
body frame, respectively, and they indicate which coordinate frame a
quantity is expressed in. The rotation matrix between these two frames
is \(R^{nb}\) , which rotates a vector from the body
frame to the navigation
frame. Further, \([a \times ]b = a\times b\)  is the skew-symmetric
matrix form of the cross-product. In conventional inertial navigation, the angular
velocity \(\omega ^b\)  and
the specific force \(s^b\)  are measured by two sensor triads consisting
of three orthogonal gyroscope and accelerometer sensors,
respectively. Then (REF ) is
time-integrated to yield estimates of \(R^{nb}\) , \(p^n\) , and \(v^n\) . The
location of the accelerometer triad defines the origin of the body frame.
